Solve the following IVP: dy dt? dy 6. + 9y = e dt 3t

Q: Solve the IVP -8 0] *-[× -16 dx dt x(t) = x, x(0) [8]

A:

Q: Solve the initial value problem. dv + sect, v(0) = 4 %3D dt 1+?

A:

Q: Find the solution to satisfying _y(t) = dy dt = 2y y(6) = 9

A: The given differential equation is; dydt=2y As we know from the integral rule,  ∫1ax+bdx=1alnax+b+C

Q: Given x= 2y? , evaluate dx dy at y = 1 and dt dt 3.

A:

Q: dx dt dy dt х — 2у + t х — у + 2t

A: The given equation is dxdt=x-2y+tdydt=x-y+2t This equation can be rewritten as x'=x-2y+t t=x'-x+2y…

Q: 1. Solve the DE as follows: d'y dy +3. +2y = 24 y(0) = 10 and y'(0) =0 dt? dt

A: Note :-  As per our guidelines , we will solve only first question for you. If you want any specific…

Q: Solve for an autonomous equation? dy/dt = f(y)

A: An autonomous first-order ordinary differential equation is an equation of the form

Q: E e dt Evaluale

A: Gamma function

Q: d?x ax dx ÷+ 9x = 0, when x(0) = 1 and (0) = 0 dt2 dt dt

A:

Q: Solve the Bernoulli equation for y. dy = 2y + y°. dt Use the following initial condition: y(0) = 1.…

A:

Q: d Vi In(t)dt equals dx

A:

Q: Solve IVP: dx x + Y, (0) = 0 dt dy 4x + Y, y (0) = 3. dt

A: Since you have posted multiple question we are supposed to give solution of first one only ...kindly…

Q: Solve the DE as follows: d²y dy +3+ +2y=24 y(0) = 10 and y'(0) = 0 dt? dt

A:

Q: dx dt -x + y + 2et ip dt — у — е-t

A: System of differential equation

Q: Solve the following differantial equation using finite difference method. d²x(1) + x(t) = 0 dt? dx…

A:

Q: b- Yt dt + dBt dY; 1-t

A:

Q: Find the solution to dy/dt = 6y Satisfying y(1)=7 y = ?

A: Firstly , separate the variables and then integrate and solve. ∫1ydy = ln(y) +C ∫tn dt =tn+1n+!+C

Q: dx dy 1. +у%3х, Зу dt dt

A:

Q: Solve the following inital value problem  (dy/dt)=t2e-y  y(0)=1

A:

Q: Solve the following initial value problem: dy dt - 3y + 21 y (0) = 10 y(t) =

A: The general solution of a differential equation always contains a constant of integration. The…

Q: 1 Solve the following Df via Laplau Transfarm Method. sint dt? with intral couditins ylu)20 y'0) =1

A: The solution is given as

Q: Find the general solution of dt z(t) = Az where z = y(t and A =

A:

Q: If æ? + y? = 25 and dy/dt = 6, find %3D dæ /dt =

A:

Q: Find all solutions of the equation: dy​/dt=yt−y−t+1. Stationary and non stationary

A:

Q: 1. Solve the DE as follows: d'y dy +3- 2 dt +2y= 24 y(0) = 10 and y'(0) = 0 dt

A:

Q: Integrate the following (a )∫eπ31cos (lnt)/t dt   and   (b) ∫2y−11/ y^2−y−6 dy

A: (a) Given integral is ∫1eπ3coslnttdt Substitute lnt=u ⇒1tdt=du And limit of integration becomes 0 to…

Q: If L= x + y dx dt and dy =3 dt what is dL dt when x=5 and y=12 Provide your answer as a decimal,…

A:

Q: Suppose you know that dy/dt = 7y and that y(0) = 4. Which of the following answers is closest to…

A: We have to solve the differential equation

Q: + iwe¬lwt = 0. dt = 0,

A: Given differential equation is

Q: Solve the following initial value problem. = - 4cos(2t + x), s'(0) = 300, s(0) = 0 dt? (Type an…

A:

Q: Vēt VE dt

A: Our Aim is to evaluate the integral given below:-

Q: dT 4 dp = 0; T=To when p= Po dp pdT

A:

Q: Solve the IVP dy/dt + 2(t + 1)y^2 = 0, y(0) = −1/8

A: To solve the IVP dy/dt +2(t+1)y²=0, y(0)=-1/8

Q: Solve the initial-value problem shown below: dy/dt=−4y/t, y(3)=5 Give an exact formula for y . y=

A: Given the IVP,

Q: S(t)e¬Jwnt dt_ 2 C =

A: In this question, we find the coefficient for the Fourier complex series cn=2T∫0Ts(t)e-jwntdt

Q: Solve the following Initial Value Problem. dy/dt=sec^2(t)-sin(t), y(pi/4)=1 y=??????????????????

A: Given that: dydt=sec2t-sint, yπ4=1

Q: | dy dt e3t +e?

A: We have to find the solution

Q: dy e, solve the IVP = 40 dt 5y y(0) = 10. - %3D 100-4t cag

A:

Q: Solve the IVP 3 d.x dx a(0) = 1, = 2. dt \t=0 dt2 dt

A: Given d2xdt2=-x(dxdt)3, x(0)=1, dxdt|t=0=2

Q: E. Find , and in terms of dx dt' dt 1. x = t°- 1 2. x = 4t + 3 y = 3t – 2 y = 4 - t

A:

Q: 2t dt J 1+e 1+et

A: By the method of substitution I have solved The integration

Q: - 0.2 t N=N,e

A:

Q: Solve the following initial value problem dy dt + 7y = u2(t), y(0) = 3

A:

Q: If eSp e = p + t, compute dp/dt when p = t = 0. p'(0)

A:

Q: Find the particular solution of this DE: dt = ev-t(1+t²) sec y; y(0) = 0 %3D

A:

Q: d?x dx + 4 + 5x – 10 = 0, when t = 0,x = 0,x = 0 %D | dt2 dt

A:

Q: t (a) y = dt Vt? +1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: S 6 ttan t dt = %3D dx Jx

A:

Q: (b) / 6dt. 2. Find (a) * dt, (c) sin 3t dt, (d) e dt.

A: solution of the given problem is below using integration formula...

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.